ECE155A Vlad Dorfman Class 10 - Solutions
Problem 1. Noise Enhancement Introduction: The problem illustrates the noise enhancement for a continuous ZF filter using the example of the Lorentzian channel. The channel s(t), AWGN noise and the equalizer g(t)
ECE155A PROBLEMS Vlad Dorfman Class #10 Due: 2/19/07
1. Noise Enhancement. Let s(t) be the Lorentzian step response of the channel ( s(t) = 1/(1+(2*t/PW50)^2) ), and suppose we design a zero-forcing linear equalizer with target z(t)=sinc(t/T). If sampled,
ECE155A Fall 07 Equalization Homework Solutions
Part I (Homework 1)
1. Note: This problem is not very clear stated. Therefore the points wont be counted. The question is restated as following: Find Z-transform and DTFT of an+m u(n), |a|<1, u(n) is a step
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Mapping User Data to Magnetic Media
Two different conventions are used to map a binary sequence, z0z1, where zi=0,1 to a magnetization pattern, w0w1, where wi=-1,+1. NRZ: zi=1 -> wi=1 , zi=0 -> wi=-1 NRZI: zi=1 represents a reversal of the direction of
ECE 154B Winter 2007 Homework #1 Due: Monday, January 22 1. In order to do some simulations, one must be able to generate samples of random variables with arbitrary probability distributions. Most programming languages have a command that generates sample
ECE 154B Winter 2007 Homework #2 Due: Monday, January 29 1. Consider the 2 hypotheses problem where the a priori probabilities for the two hypotheses are: 0 = and 1 = . Let the conditional probability densities of the observable Y under the two hypotheses
ECE 154B Winter 2007 Homework #3 Due: Monday, February 5, 2007 1. Prove that for M a positive even integer, 12 +32+(M-3)2 + (M-1)2 = M(M2-1)/6. (Hint: Use induction) 2. The following applies to M= 4, PAM transmission with unequal a priori probabilities. A
ECE 154B Homework #4 Due: February 12, 2007 1. Problem 8.1 from Ziemer and Tranter 2. Problem 8.12 from Ziemer and Tranter 3. Problem 8.13 from Ziemer and Tranter 4. Problem 8.17 from Ziemer and Tranter (Assume M=22m, m an integer) 5. Problem 8.1 from Zie
ECE 154B Winter 2007 Homework #5: Due February 28, 2007 1. Consider that the Voronoi region for a 2-D signal is a hexagon centered at the signal point with shortest distance from the center to any of the edges of the hexagon equal to 2. Assume AWGN with z
ECE 154B Homework #6 Due March 7, 2007 1. Making the usual assumptions of equally likely signals in AWGN and an optimal receiver, it can be shown that the probability of symbol error for M/2 orthogonal signals of energy E and their negatives is given as:
ECE 154B Homework #7 Due March 14, 2007 1. Consider the transmission of two FSK sinusoidal signals whose frequencies are chosen
such that the signals are orthogonal. Let the amplitude of each signal be A, the duration of each signal be T, and the energy o
ECE 154B Winter 2007 Homework #1 Solutions 1. In order to do some simulations, one must be able to generate samples of random variables with arbitrary probability distributions. Most programming languages have a command that generates samples for a random
ECE 154B Winter 2007 Homework #2 Solutions 1. Consider the 2 hypotheses problem where the a priori probabilities for the two hypotheses are: 0 = and 1 = . Let the conditional probability densities of the observable Y under the two hypotheses be: fY|0(y) =
ECE 154B Winter 2007 Homework #3 Due: Monday, February 5, 2007 1. Prove that for M a positive even integer, 12 +32+(M-3)2 + (M-1)2 = M(M2-1)/6. (Hint: Use induction) Proof by induction: Let M=2. (2-1)2=(2)(2)2-1)/6=1. Assume true for M. Test for M+2: 12 +
ECE 154B Homework #4 Due: February 12, 2007 1. Problem 8.1 from Ziemer and Tranter Rb = log 2 M R s bps M = 4 , Rb= 2 2000= 4000 bps M =8 , Rb=3 2000 =6000 bps M =64 , Rb=6 2000 =12000 bps 2. Problem 8.12 from Ziemer and Tranter The signal points lie on a
ECE 154B Homework #6 Solutions 1. Making the usual assumptions of equally likely signals in AWGN and an optimal receiver, it can be shown that the probability of symbol error for M/2 orthogonal signals of energy E and their negatives is given as: P[symbol
ECE 154B Homework #7 Solutions 1. Consider the transmission of two FSK sinusoidal signals whose frequencies are chosen
such that the signals are orthogonal. Let the amplitude of each signal be A, the duration of each signal be T, and the energy of each si
ECE155A Fall 07 Lecturer Dr. Vlad Dorfman Class #8
Equalization - Homework Due Oct 29, 2007, 10 points each
1. Find Z-transform and DTFT of am u(n), |a|<1, u(n) is a step function , u(n) =0 for n<0 and u(n)=1 for n>1. 2. Derive the formula for the sum of